It is known, from, for example BBC Research Department Report “Video noise reduction” BBC RD 1984/7 N. E. Tanton et al., July 1984, that random noise in a sequence of television images, or some other kinds of electronically generated images, e.g. scanned film, can be reduced by applying a recursive temporal filter which operates on each picture element hereinafter abbreviated to ‘pel’. It is beneficial to reduce noise levels prior to viewing images but it is also beneficial prior to processes that are sensitive to the presence of noise, especially compression systems such as those defined by, but not limited to, MPEG specifications. In practice, noise control is among several important and valuable techniques employed in pre-processing elements inherent in modern compression hardware and software realisations of these specifications.
For each pel indexed in an image by i, an output R(i) of a recursive filter is a sum of complementary proportions of a current image C(i) and a previous resultant output image S(i), such that proportions of C(i) and S(i) in the output R(i) are controlled by means of a fractional parameter K. If this notation is extended with a suffix ‘f’ to denote the frame, it is evident that the condition Sf(i)=Rf−1(i) ensures a first order recursive temporal filter operation.
Hence, each pel in the result R(i) is expressed as:Rf(i)=K·Cf(i)+(1−K)·Sf−1(i)0≦K≦1